Quote:
Originally Posted by

**aleksandr**
For perpetual calendars, don't they just have to be accurate to 4 years only to account for leap years? Or am I missing something..

This is what I found on Wikipedia:

The **Gregorian calendar**, also called the **Western calendar** and the **Christian calendar**, is the internationally accepted civil calendar.^{[1]}^{[2]}^{[3]} It was introduced by Pope Gregory XIII, after whom the calendar was named, by a decree signed on 24 February 1582; the decree, a papal bull, is known by its opening words, *Inter gravissimas*.^{[4]} The reformed calendar was adopted later that year by a handful of countries, with other countries adopting it over the following centuries.

The motivation for the Gregorian reform was that the Julian calendar assumes that the time between vernal equinoxes is 365.25 days, when in fact it is presently almost exactly 11 minutes shorter. The discrepancy accumulates at the rate of about three days every four centuries, resulting in the equinox being on March 11 (a cumulative error of about 10 days since Roman times), and moving steadily earlier in the Julian calendar, at the time of the Gregorian reform. Because the spring equinox was tied to the celebration of Easter, the Roman Catholic Church considered this steady movement in the date of the equinox undesirable.

The Gregorian calendar reform contained two parts: a reform of the Julian calendar as used prior to Pope Gregory's time and a reform of the lunar cycle used by the Church, with the Julian calendar, to calculate the date of Easter. The reform was a modification of a proposal made by the Calabrian doctor Aloysius Lilius (or Lilio).^{[5]} Lilius' proposal included reducing the number of leap years in four centuries from 100 to 97, by making 3 out of 4 centurial years common instead of leap years: this part of the proposal had been suggested before by, among others, Pietro Pitati. Lilio also produced an original and practical scheme for adjusting the epacts of the moon when calculating the annual date of Easter, solving a long-standing obstacle to calendar reform.

The Gregorian calendar thus modified the Julian calendar's regular cycle of leap years, years exactly divisible by four,^{[6]} including all centurial years, as follows:

Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100; the centurial years that are exactly divisible by 400 are still leap years. For example, the year 1900 is not a leap year; the year 2000 is a leap year.^{[7]}

In addition to the change in the mean length of the calendar year from 365.25 days (365 days 6 hours) to 365.2425 days (365 days 5 hours 49 minutes 12 seconds), a reduction of 10 minutes 48 seconds per year, the Gregorian calendar reform also dealt with the accumulated difference between these lengths. Between AD 325 (when the First Council of Nicaea was held, and the vernal equinox occurred approximately 21 March), and the time of Pope Gregory's bull in 1582, the vernal equinox had moved backward in the calendar, until it was occurring on about 11 March, 10 days earlier. The Gregorian calendar therefore began by skipping 10 calendar days, to restore March 21 as the date of the vernal equinox.

Because of the Protestant Reformation, however, many Western European countries did not initially follow the Gregorian reform, and maintained their old-style systems. Eventually other countries followed the reform for the sake of consistency, but by the time the last adherents of the Julian calendar in Eastern Europe (Russia and Greece) changed to the Gregorian system in the 20th century, they had to drop 13 days from their calendars, due to the additional difference between the two calendars accumulated after 1582.

The Gregorian calendar continued the previous year-numbering system (*Anno Domini*), which counts years from the traditional date of the nativity, originally calculated in the 6th century and in use in much of Europe by the High Middle Ages. This year-numbering system, now also called Common Era, is the predominant international standard today. ^{[8]}

^{The Gregorian calendar is an arithmetical calendar potentially extending over an infinite time scale. It consists of a series of contiguous calendar years identified by consecutive year numbers.[9] It is a solar calendar and counts days as the basic unit of time, grouping them into years of 365 or 366 days; and repeats completely every 146,097 days, which fill 400 years, and which also happens to be 20,871 seven-day weeks.[10][11]}

^{Of these 400 years, 303 common years have 365 days and 97 leap years have 366 days. This yields a calendar mean year of exactly 365+97/400 days = 365.2425 days = 365 days, 5 hours, 49 minutes and 12 seconds. The same result is obtained by summing the fractional parts implied by the rule: 365 + 1⁄4 − 1⁄100 + 1⁄400 = 365 + 0.25 − 0.01 + 0.0025 = 365.2425}

^{A Gregorian year is divided into twelve months:}

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^{Although the month length pattern seems irregular, it can be represented by the arithmetic expression L = 30 + { [ M + floor(M/8) ] MOD 2 }, where L is the month length in days and M is the month number 1 to 12. The expression is valid for all 12 months, but for M = 2 (February) adjust by subtracting 2 and then if it is a leap year add 1.}

^{For a better representation, consider Zeller's Congruence.}

^{A calendar date is fully specified by the year (numbered by some scheme beyond the scope of the calendar itself), the month (identified by name or number), and the day of the month (numbered sequentially starting at 1).}

^{Leap years add a 29th day to February, which normally has 28 days. The essential ongoing differentiating feature of the Gregorian calendar, as distinct from the Julian calendar with a leap day every four years, is that the Gregorian omits 3 leap days every 400 years. This difference would have been more noticeable in modern memory were it not that the year 2000 was a leap year in both the Julian and Gregorian calendar systems.}

^{The intercalary day in a leap year is known as a leap day. Since Roman times 24 February (bissextile) was counted as the leap day,[12][13] but now 29 February is regarded as the leap day in most countries.}

^{Although the calendar year runs from 1 January to 31 December, sometimes year numbers were based on a different starting point within the calendar. Confusingly, the term "Anno Domini" is not specific on this point, and actually refers to a family of year numbering systems with different starting points for the years.}

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